Wednesday, June 11, 2008

Once more

Since the world no longer needs a good 10 cent cigar, and the White Owls Dad and Grandpa Rabett thought were good were anything but, Eli is driven to again try and provide a relatively simple explanation of the greenhouse effect.

For those of you who crave death by mathematical physics the bunnies suggest Ray Pierrehumbert's on line text book, or in a somewhat (and I warn you, only somewhat) simpler form in an arXiv article by Arthur Smith.

Eli will alter the text based on suggestions however we are going to KEEP IT SIMPLE. All entries become the property of Rabett Labs.

  1. The total energy emitted by the earth has to equal the total energy absorbed from the sun. The only mechanism for either of these processes is radiation to and from space
  2. The earth radiates in the infrared, the sun radiates at much shorter wavelengths, principally in the visible.
  3. It gets colder the higher you go in the troposphere and the density of molecules is lower.
  4. From 3 the rate of radiation from IR active (greenhouse gas, GHG) molecules (CO2, H2O, CH4) is lower the higher you go (hotter things radiate more, see Stefan-Boltzmann law, more molecules radiate more).
  5. In the atmosphere below 100 km there is always a local effective temperature, thus the absorbtivity of the GHGs equals its emissivity (Kirchhoff's law)
  6. Greenhouse gases are IR absorbers/emitters. They effectively block radiation escaping to space at wavelengths they absorb EXCEPT at high enough levels where the gas density is low and the radiation can escape directly to space without being absorbed by other GHG molecules(this is about 7 km which is still in the troposphere).
  7. Because radiation to space is blocked at IR wavelengths where GHGs (and clouds) absorb, the surface has to warm so that radiation can increase in unblocked areas of the spectrum and escape to space.
  8. This means that there will also be increased radiation in regions of the spectrum where greenhouse gases absorb which, in turn, will warm the atmosphere but cannot escape to space. Radiation absorbed in the atmosphere and scattered back to the surface, warming the surface yet further.
  9. As the atmosphere warms, the areas of the spectrum where the greenhouse gas molecules absorb widens as more energetic levels of the GHG are populated (The link points to on line software, which you can model this yourself)
There are two complementary mechanisms

Walking Mechanism
. Increasing the amount of GHGs widens the spectral regions where they absorb and narrows the windows where radiation can escape to space. To maintain balance with incoming solar, the atmosphere and surface warm further

and Chewing Gum Mechanism. As the GHG mixing ratio increases, the effective level at which the Earth can radiate to space at the wavelengths emitted by the GHGs climbs, but because of the cooling with altitude and the lower density of molecule, to maintain the same radiation rate and balance the solar input, the new higher level at which the earth radiates has to warm, and to do this the entire troposphere and the surface have to warm.

Since the increase of CO2, methane, nitrous oxide, and other GHGs are known to be caused by humans, so must an increase in surface temperature driven by these mechanisms.

Does the greenhouse effect operate by the same mechanism as greenhouses? No (except if you think of one blocking off energy loss by closing regions of the spectrum for radiative loss, and the other blocking off energy loss by stopping convection)


Anonymous said...

anon 11.17

This is clear and straightforward and 'just physics'.

Question, if this is all that is happening, how much surface warming would a rise in CO2 from 300 to 600 ppm cause due to this effect, and how much of it has already happened? Not, how much warming has happened, but how much of this effect has already happened? The first extra 100 ppm have more effect than the next 100, if I understand correctly?

I know this is not all that is happening, but would appreciate walking through it one step at a time because its quite hard to follow as usually explained.

Anonymous said...

I can see how someone might debate the value of the climate sensitivity to CO2 doubling, but "debating" the very existence of the greenhouse effect?

Good grief, that's too kooky for words. Right up there with the debate about how many angels fit on the head of pin.

Anonymous said...

anon 11.17

Don't know if this referred to my post, but it was not intended to debate the existence of the greenhouse effect. Obviously its real, that is just physics. The questions are about how it works exactly, how much is due to the mechanism Eli outlined, how much to other consequent factors, how much has already happened since eg 1950 or whenever....

Hope not to have given any impression of doubting its existence!

Arthur said...

Eli - I'm flattered, but curious what brought this up. Have our Germans been causing trouble again somewhere?

BTW - ever hear Tom Lehrer's "MLF lullaby" (from "That was the year that was", 1968)

--- "Once all the Germans were warlike and mean, But that couldn't happen again. We taught them a lesson in nineteen eighteen, And they've hardly bothered us since then."

(my mother's German, I have to tease her sometimes :-)

EliRabett said...


No, but this comes up periodically especially on the more political blogs and I need an explanation that mom can understand. It also seemed important to point out that there are two mechanisms. Explanations usually only consider one. I think the lifting of the emission level is the more important one (it's obviously the only one for a grey atmosphere), but does anyone have any figures??

Anonymous said...

anon 11.17

Well, it must be a politically incorrect question, but what seems to be missing from the explanation is something along the lines:

And so, doubling CO2 from 300 to 600 ppm results in a direct rise in temperature from these effects of [X].

In addition, there is a further rise in temperature of [Y] from effects [Z].

With the blanks filled in.

Anonymous said...

Those whom Arthur Smith was addressing challenge the very existence of an atmospheric greenhouse effect.

Just dumb.

All I can figure is German universities must have much lower standards than the US.

It used to be that German universities produced some of the best and brightest.

Now we get all this rubbish about "no greenhouse effect", "no such thing as a global average temp", "Stern is a fool" and other such quackery coming out of German Universities. Really makes you wonder.

EliRabett said...

Anon, not the question. The question was what the mechanism is.

If you want Eli to write an IPCC report please remit funding. Rabett Labs will be pleased to undertake this effort for costs plus an overhead rate of 1.5 kg carrots per day per bunny and 25% for the bank account. Ms. Rabett is still on travel in expensive corners of the world.

FWIW the central estimate of total global warming on 2x CO2 is 3 C. The range of the estimates is between 2 and 5 C. There is a small but small (although disasterous) tail on the high end.

Of that about 1/3 is a direct effect of 2x CO2 and 2/3 is indirect, mostly from increasing water vapor pressure.

There are a zillion posts on this on the web. Google em. There are not very many good and simple ones on estimates.

Magnus said...

Don’t forget the ”But CO2 is in a so low concentration it can’t make any difference!” which seems frequent on political blogs...

Anonymous said...

anon 11.17

Thanks for the explanation. Now all you need do is add something like the following to your own account:

And so, doubling CO2 from 300 to 600 ppm results in a direct rise in temperature from these rises in CO2 of 0.7 C.

In addition, there is a further rise in temperature of between roughly 2 and 4 degrees from the rising water vapor pressure which the 0.7 rise produces.

Your explanation is now much more complete, and is no longer open to the denialist canard mentioned by magnus that the rise in CO2 cannot possibly lead to the consequences claimed. Of course it can, by giving rise to other effects. You might care to add some explanatory sentence to this effect, such as the following:

The rise in CO2 is not disastrous in itself. It is the trigger for disastrous consequences. The force exerted by a finger on a trigger is not lethal. It is what it releases that is lethal.

Mitchell said...

I agree with anonymous 11:59. It was a real surprise to me to learn that most of the projected warming comes from the feedbacks, not just from CO2 acting as a heat reservoir. If you want an educated public, they need to know what climate sensitivity is and why it's 3 degrees rather than 1 degree.

CapitalistImperialistPig said...


Since you were kind enough to critique my attempt at a simple explanation of GHG induced warming let me return the favor. I have a few quibbles, but especially #9. Increased opacity due to temperature change is a significant effect for Venus, but for Earth? I doubt it. The narrowing of the transparency windows is due not to temperature change but to concentration change - opacity in the edges of the of the windows increases due to increased concentration of the absorber.

Temperature change effects on opacity are not necessarily simple. For water vapor, the effect can be inverse, possibly due to increasing dimerization of water at low temperatures.

Anonymous said...

It was a real surprise to me to learn that most of the projected warming comes from the feedbacks, not just from CO2 acting as a heat reservoir."

Actually, CO2 does not act like a heat reservoir.

In fact, it gives up most of the absorbed energy very quickly (to other molecules in the air, mainly Nitrogen and Oxygen), which is why it is such an effective greenhouse gas. Each molecule of CO2 absorbs and then very quickly re-emits, making it available to absorb more energy and re-emit. if each CO2 molecule held onto the energy (ie, acted as a reservoir), CO2 would not be a very effective greenhouse gas.

but the part about feedbacks is a key point.

CapitalistImperialistPig said...


I don't like #5 much either:
In the atmosphere below 100 km there is always a local effective temperature, thus the absorbtivity of the GHGs equals its emissivity (Kirchhoff's law)

I'm guessing that you are referring to Local Thermodynamic Equilibrium (LTE). The atmosphere is not generally in LTE at any level, but if we restrict our attention to thermal wavelengths it can be when scattering isn't important. That should be true if we are above the clouds and below the region where molecular collisions are rare enough to permit significant departures from thermal equilibrium (100 km?)

EliRabett said...

The excited CO2 molecule gives up its energy by collisional energy transfer with nitrogen and oxygen. The vibrational excitation is transformed into kinetic energy (heat).


Anonymous said...

RE claim that "The atmosphere is not generally in LTE at any level"

Practically speaking, it seems to me that LTE does hold for air near the earth's surface.

A molecule in the air (eg, Oxygen) will collide with another molecule long before it can reach a region with an appreciably different temperature.

For oxygen at STP, for example, the mean free path is about 0.1 micron.

I doubt it even makes any sense to talk about the temperature change over 0.1 micron.

EliRabett said...

You can demonstrate LTE up through the stratosphere and into the mesosphere. It's only when you get into the ionosphere that it really fails. Basically it will hold anywhere the radiative lifetime is much longer than the average time between collisions

CapitalistImperialistPig said...

Anon and Eli,

In the lower atmosphere LTE fails not because molecules aren't thermalized but because they aren't in thermal equilibrium with visible radiation. The source function has a scattering term! See, e.g., Chandrasekhar's Radiative Transfer where all this is explained in the first ten pages or so.

This is not much of a problem if that atmosphere is relatively clear and clean (because the scattering term is small enough to be neglected), but it is a problem in cloud, fog, dust, etc.

CapitalistImperialistPig said...

Just for the heck of it, my $0.10 explanation.

(1)The Earth's atmosphere is heated from the surface, because sunlight goes right through it.
(2) It cools from above, since infrared radiation doesn't go through CO2 well.
(3)Adding more CO2 adds more insulation, and makes the Earth hotter at the surface for the same reason that wrapping yourself in a blanket makes you warmer.

Anonymous said...

"they aren't in thermal equilibrium with visible radiation"

This table shows the mean time between collisions for atmospheric constituents at 1 atmosphere and 0C

for CO2 it is about 100 ps, which is roughly 1/100th the mean radiative time. So virtually all the CO2 molecules are going to collide (and presumably transfer their energy to other molecules) before they have a chance to radiate.

So I think Eli is right. I don't think it is correct to say that the atoms are not in equilibrium in the case of air near the earth's surface. The relevant numbers would seem to indicate that they are.

Anonymous said...

I also have a two-part series on this, no mathematics:

EliRabett said...

Pig, the atmosphere would be in thermal equilibrium IF it were in equilibrium with the radiation field. However, because radiation absorption and emission are effectively decoupled from collisional energy transfer, and the later is much faster than interaction with radiation, LTE obtains and you can define temperatures. You are confusing equilibrium and LTE much like Chris Essex.

Effectively you can define LTE as a condition in which the distribution of energy among the states is Boltzmann with the same temperature for all modes of motion. That's the way it is up to about 100 km.

Also the radiative lifetime of CO2 is a lot longer than 100 nanoseconds

CapitalistImperialistPig said...


I think you are missing my point. Molecular equilibration time is irrelevant to the fact that a scattering atmosphere can depart from LTE. You can't be in LTE if the source function is not Planckian. Since the scattered photons in this case have a much different spectrum from the thermal photons, emission and absorption are no longer proportional.

It is also not true that radiation absorption and emission are effectively decoupled from collisional energy transfer in the lower atmosphere - if they were there would be no collisional line broadening.

Anonymous said...

anon 11.17

"(3)Adding more CO2 adds more insulation, and makes the Earth hotter at the surface for the same reason that wrapping yourself in a blanket makes you warmer."

CIP, that is not at all how it works. That is not what the role of CO2 is in the process.

If you say this, you lay yourself open to the denialist objection that the power of CO2 is insufficient to produce the warming which you are forecasting. And this is true, so you will find it a hard objection to meet. However, it is completely irrelevant!

What CO2 does is to produce a small amount of initial warming. This small initial warming then produces a much larger later amount, because it leads to the release of further greenhouse gasses in the form of water vapor.

It is very important to make this point, to rebut the other idiotic denialist argument. This is that water vapor and not CO2 is the most powerful and abundant greenhouse gas. This is also true, but it is also irrelevant.

It may be that the analogy of the blanket will help people understand what is going on, but the attribution of the blanket's warmth solely to CO2 will not. If you want to explain it in these terms, you need to use some other analogy. It is more like, a parent sees a child pulling up the sheet, realized it is cold, and so puts a quilt over.

Actually, the planet is far more sensitive to small temperature increases than people generally realize. This point has to be made very strongly. It is why the relatively small amount of recent warming is taking us over the tipping point.

Anonymous said...


OK, I should have said GHG instead of CO2, but the fact is that any simplified explanation, is vulnerable to skeptical critique.

Tipping point arguments are very vulnerable to critique, because we have evidence from past warmings and coolings that the Planet has regulated itself, albeit crudely.


Anonymous said...

Am i wrong in thinking that one does not strictly need LTE for the calculation; all one needs is detailed balance ?


Anonymous said...

I apologize for being an LTE nitpicker, since I think that it's hardly relevant to the global warming question (cooling by volcanic dust is probably an exception).


Anonymous said...

CIP says "we have evidence from past warmings and coolings that the Planet has regulated itself, albeit crudely."

This is typical denialist propaganda of a most nefarious sort, and its disturbing you've given it any credence. Denialists have got this one wrong in one of their usual ways, they have inverted the evidential direction. We know that the planet is hypersensitive to small warmings. Therefore had there been warmings in the past of 0.7 or so degrees, they would, we know, have led to the trigger effect, so that a period of disastrous warming would have occurred.

However, such disastrous warmings have not occurred in historical times. It follows that no warmings of that sort took place. The MWP and Roman warmings were obviously regional phenomena - this is the proof of it. If you like, they were prolonged episodes of weather. The LIA was confined to the UK and parts of Europe. When Napoleon retreated from Russia, he was the victim of weather, as have been many invaders of Russia.

We know from the Philosophy of Science that there are no theory free observations, and certainly so called observations of previous climate fluctuations are not among them.

EliRabett said...

Pig, nothing wrong in picking nits. The reason that I mentioned it is that you need LTE or E to have a temperature. On balance it is something I should take out. Having this discussion with mom would not be a fruitful thing.